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Deduction theorems within RM and its extensions

Published online by Cambridge University Press:  12 March 2014

J. Czelakowski  and
W. Dziobiak
J. Czelakowski
Affiliation:
Department of Mathematics, Opole University, 45-951 Opole, Poland E-mail: jczel@sparc-1.uni.opole.pl
W. Dziobiak
Affiliation:
Departament of Mathematics, University of Puerto Rico, Mayagüez Campus, Mayagüez, PR 00681-5000, E-mail:, w.dziobiak@rumac.upr.clu.edu
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Abstract

In [13], M. Tokarz specified some infinite family of consequence operations among all ones associated with the relevant logic RM or with the extensions of RM and proved that each of them admits a deduction theorem scheme. In this paper, we show that the family is complete in a sense that if C is a consequence operation with CRM ≤ C and C admits a deduction theorem scheme, then C is equal to a consequence operation specified in [13]. In algebraic terms, this means that the only quasivarieties of Sugihara algebras with the relative congruence extension property are the quasivarieties corresponding, via the algebraization process, to the consequence operations specified in [13].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 64 , Issue 1 , March 1999 , pp. 279 - 290
Copyright
Copyright © Association for Symbolic Logic 1999

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References

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